For scalar and gravitational perturbations, the asymptotic (high overtone) values of \(\omega \)  have been calculated analytically in equation (3.39) of [1]} (and also equation (3.39) of [2]}) asWe have changed the indexing in [1]}, which is completely arbitrary, to match that in our tables.:
\(\omega \eta = (n-1) \pi +\frac{5\pi }{4} + \frac{i}{2} \ln 2.\) 
